Damped shm successive amplitude ratio

In summary, the damped frequency (f) is 100 Hz and the ratio of the amplitude of two successive maxima is one half. The undamped frequency (W) can be found using the equation w = (W^2 - c^2)^1/2, where c is the damping factor. Despite the damped frequency being constant, the amplitude decreases in a damped SHM. To find the frequency without damping, one can use the information about the ratio of successive maxima and the damping factor in the equation.
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Question: The damped frequency (f) is 100 Hz. The ratio of the amplitude of two successive maxima is one half. What is the undamped frequency?

My first problem is I don't understand the basic equations I'm working with. If W is the undamped angular frequency and w is the damped frequency, I was told that w = (W^2 - c^2)^1/2 where c is the damping factor. I have a problem with this however because the right side of the equation is a constant (W and c are obviously both constant) and yet the damped frequency w is constantly decreasing in a damped SHM. What's going on here?
 
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  • #2
The frequency of the damped oscillator is constant. What is decreasing is the amplitude.

To answer your problem: What is the relation between the amplitude of successive maxima in terms of the frequency and the damping? How can you use this information to find the frequency if you removed the damping (i.e., how do you get W)?
 

1. What is damped SHM successive amplitude ratio?

Damped SHM (simple harmonic motion) successive amplitude ratio is a measure of the decrease in amplitude of a damped harmonic oscillator over successive cycles. It is used to quantify the rate at which the amplitude decreases in damped SHM systems.

2. How is damped SHM successive amplitude ratio calculated?

The damped SHM successive amplitude ratio is calculated using the formula An+1/An, where An+1 is the amplitude of the (n+1)th cycle and An is the amplitude of the nth cycle.

3. What does a high damped SHM successive amplitude ratio indicate?

A high damped SHM successive amplitude ratio indicates a faster decrease in the amplitude of the oscillator over successive cycles. This could be due to a higher level of damping in the system.

4. How does damped SHM successive amplitude ratio relate to the quality factor?

The damped SHM successive amplitude ratio is inversely proportional to the quality factor (Q) of the system. This means that as the damped SHM successive amplitude ratio increases, the quality factor decreases, indicating a less efficient oscillation.

5. What are some real-life applications of damped SHM successive amplitude ratio?

Damped SHM successive amplitude ratio is used in various fields such as mechanical engineering, electrical engineering, and physics to analyze and understand the behavior of damped harmonic oscillators. It is also used in the study of musical instruments and earthquake engineering.

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